The rising action is one of the elements of plot postulated by the German writer Gustav Freytag, in Techniques of Drama (1863). The rising action leads to the turning point in the story, which is called the climax. Thus, the rising action includes all of the events that lead to the climax.
For an example of the rising action, think of the children's story, "Little Red Riding Hood." The climax of the story is when Little Red Riding Hood discovers that her granny has been replaced by the Wolf, who has disguised himself to deceive the little girl. All of the action that leads up to this climax (packing the basket of food, setting out to Granny's house, initially encountering the Wolf in the forest, etc.) are all part of the rising action.
The rising action is the series of events that lead up to the climax. It occurs after your introduction. The rising action creates the tension and action necessary to make the climax the cultivating moment in the work. The rising action gives a background to the climax; without it, the climax would not seem placed on any solid foundation.
For example, in Death of a Salesman, the rising action includes Willy getting fired, Biff divulging that he knows Willy is a fake, Biff being turned down by Willy's old boss and stealing something, etc. All of these events lead up to the climax, in which Willy and Biff have an incredible argument that culminates in Willy killing himself.
Each of these events put one more thing on Willy's plate; they 'rose' the action of the story. This all lead to the big blow-up, the climax, of the story.
A traditional dramatic plot structure has five elements: Exposition, Complication, RISING ACTION, Climax and Resolution. The Exposition introcuces the main character and the initial situation. A complication arises that calls the main character's future in doubt--Suspense or tension is created. The Rising Action runs through the middle part of the plot structure and each detail of it increases the suspense, making one side or the other seem the likely outcome. (The main character will succeed or fail.) The Climax is the moment in which the suspense is brought to an end. The tension is suddeenly released. The Resolution is the wrapping up of loose ends. This structure is also called Fryetag's Triangle.